10.1.6 problem 6

Internal problem ID [1103]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.1. Page 40
Problem number : 6
Date solved : Saturday, March 29, 2025 at 10:39:02 PM
CAS classification : [_linear]

\begin{align*} 2 y+t y^{\prime }&=\sin \left (t \right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

ode:=2*y(t)+t*diff(y(t),t) = sin(t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {\sin \left (t \right )-\cos \left (t \right ) t +c_1}{t^{2}} \]

✓ Mathematica. Time used: 0.034 (sec). Leaf size: 19

ode=2*y[t]+t*D[y[t],t]== Sin[t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {\sin (t)-t \cos (t)+c_1}{t^2} \]

✓ Sympy. Time used: 0.319 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t*Derivative(y(t), t) + 2*y(t) - sin(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {\frac {C_{1}}{t} - \cos {\left (t \right )} + \frac {\sin {\left (t \right )}}{t}}{t} \]